一类互惠共存系统的定态分歧与稳定性

一类互惠共存系统的定态分歧与稳定性李大华，傅一平（华中理工大学数学系，武汉４３００７４）基金项目：国家自然科学基金资助项目．１）现在江西省九江师范专科学校工作，邮政编码３３２０００．１９９２年５月６日收到．一、引言在文［１］中Ｒ．Ｍ．Ｍａｙ提出了一个...     

平面上全局半稳定系统

平面上全局半稳定系统郑作环（海南师范学院数学系，海口５７１１００）１９９０年６月２日收到，１９９１年８月２８日收到修改稿．一、前言设函数Ｘ（ｘ，ｙ）与Ｙ（ｘ，ｙ）在平面Ｒ２上连续，又设微分方程组满足解对初始值的连续依赖性条件，记ｆ（ｐ，ｔ）为（１）式...     

截断分布族下参数和损失的可容许估计的几点注记

截断分布族下参数和损失的可容许估计的几点注记吴启光，何敏（中国科学院系统科学所，北京１０００８０）国家自然科学基金资助课题．１９９２年６月２０日收到，１９９３年２月１日收到修改稿．一、引言考虑截断分布族，其分布密度函数为其中为参数，参数空间为一区间（...     

一类化学反应系统的极限环

一类化学反应系统的极限环吴檀，井竹君（北京科技大学基础部，北京１０００８３）（中国科学院数学研究所，北京１０００８０）本文讨论三次系统极限环的存在性。文献［１］指出（１）是一类化学反应系统的一个模型，且讨论了当而，ｃ＝１时，系统（１）极限环的存在性，...     

非等谱Lax算子族的Virasoro代数

非等谱Ｌａｘ算子族的Ｖｉｒａｓｏｒｏ代数马文秀（复旦大学数学研究所，上海２００４３３）国家博士后科学基金资助项目．１９９１年７月２５日收到．１９９２年７月６日收到修改稿．一、引言Ｌａｘ算子方法［１］在可积系统理论中有着广泛的应用．从一个谱问题出发我们...     

鲁棒稳定多项式的摄动界

鲁棒稳定多项式的摄动界安森建,王恩平（中国科学院系统科学研究所,北京１０００８０）基金项目：国家自然科学基金资助项目．１）作者现在通讯地址：北京大学力学系,邮政编码：１００８７１．１９９２年１月００４日收到,１９９２年４月７日收到第一次修改稿,１９９...     

论多目标分式规划

论多目标分式规划徐增堃（浙江师范大学数学系，金华３２１００４）基金项目：浙江省教委自然科学基金资助课题．１９９０年１０月２９日收到，１９９１年１０月５日收到第一次修改稿．１９９２年９月７日收到第二次修改稿，１９９３年２月１３日收到第三次修改、压缩稿．...     

回归曲线的加权正交级数估计

回归曲线的加权正交级数估计杨瑛（北京大学概率统计系，北京１００８７１）国家自然科学基金资助项目．１９８９年１２月３日收到．１９９０年１１月２２日收到第一次修改稿．１９９２年８月７日收到第二次修改稿．一、引论自１９６２年Ｃｅｎｃｏｖ［１］提出了密度函数...     

可压核废料污染问题的数值方法

可压核废料污染问题的数值方法李潜（山东大学数学系，济南２５０１００）国家自然科学基金资助项目．１９９１年１１月４日收到，１９９２年６月１６日收到修改压缩船．一、引言多孔介质中，可压缩核废料污染问题的数学模型是下述抛物型方程组的初边值问题［１］其中ｐ是...     

投影绝对中位离差估计及其应用

投影绝对中位离差估计及其应用崔恒健，田玉斌（北京师范大学，１００８７５）国家自然科学基金资助项目１９９１年６月８日收到，１９９２年９月５日收到修改稿．一、引言与记号设Ｙ；，Ｙｚ，…，Ｙ。ｉ．ｉ．ｄ．一Ｙ为１维ｒ．ｖ，记Ｈ为Ｙ的分布函数，Ｈ。为其经验分...     

A theory for synchronization of dynamical systems

In this paper, a theory for synchronization of multiple dynamical systems under specific constraints is developed from a theory of discontinuous dynamical systems. The concepts on synchronization of two or more dynamical systems to specific constraints are presented. The synchronization, desynchronization and penetration of multiple dynamical systems to multiple specified constraints are discussed, and the necessary and sufficient conditions for such synchronicity are developed. The synchronicity of two dynamical systems to a single specific constraint and to multiple specific constraints is investigated. Finally, the synchronization and the corresponding complexity for multiple slave systems with multiple master systems are discussed briefly. The meaning of synchronization for dynamical systems with constraints is extended as a generalized, universal concept. The theory presented in this paper may be as a universal theory for dynamical systems. The paper provides a theoretic frame work in order to control slave systems which can be synchronized with master systems through specific constraints in a general sense.     

THE V-FUNCTIONAL METHOD FOR THE STABILITY OF DEGENERATE DIFFERENTIAL SYSTEMS WITH DELAYS

1 IntroductionStability is an important perfermance index of concrete systems such asmanagement systems, power systems, engineering systems and so on. Forthe stability V--functional criterion method of functional differential systems,have had many results in recent years, see) for example, [1] and [2]. Andfor degenerate systems, papers [41-[81 have carefully discussed and given someimportant results. But we note that (see [9]) many concrete systems, besidescontain delay, are degenerate. So, f…     

Reduced order observer design for nonlinear systems

This work is a geometric study of reduced order observer design for nonlinear systems. Our reduced order observer design is applicable for Lyapunov stable nonlinear systems with a linear output equation and is a generalization of Luenberger’s reduced order observer design for linear systems. We establish the error convergence for the reduced order estimator for nonlinear systems using the center manifold theory for flows. We illustrate our reduced order observer construction for nonlinear systems with a physical example, namely a nonlinear pendulum without friction.     

Hyperbolic systems of conservation laws with a symmetry

Hyperbolic systems of conservaiton laws with a symmetry are studied. Some peculiar phenomena for such systems are shown. Admissibility criteria for solutions to such systems are discussed. propagation and cancellation of initial oscillations for the systems are classified. As a byproduct of this study, an existence theorem of global solutions for the Cauchy of the systems is established.     

Reduced order observer design for discrete-time nonlinear systems

This work is a geometric study of reduced order observer design for discrete-time nonlinear systems. Our reduced order observer design is applicable for Lyapunov stable discrete-time nonlinear systems with a linear output equation and is a generalization of Luenberger’s reduced order observer design for linear systems. We establish the error convergence for the reduced order estimator for discrete-time nonlinear systems using the center manifold theory for maps. We illustrate our reduced order observer construction for discrete-time nonlinear systems with an example.     

On stability for switched linear positive systems

This paper addresses the stability properties of switched linear positive systems in continuous-time as well as in discrete-time. In the discrete-time case, some sufficient and necessary conditions for asymptotic stability are derived for pairs of second order systems. Similar conditions are also established for a finite number of second order systems. Furthermore, for higher order systems, some results on stability are provided in a similar manner. In particular, in this case, a common linear Lyapunov function guaranteeing the stability of the switched positive systems can be easily located by means of geometry properties. In the continuous-time case, a finite number of second order systems are considered. Some equivalent conditions for stability of such systems are developed.     

Controllability and observability of coordinated linear systems

This paper develops concepts of controllability and observability for the class of coordinated linear systems, a special class of linear hierarchical systems with a top-to-bottom information structure. The usual concepts of reachability and indistinguishability for linear systems are refined, taking into account the decentralized nature of coordinated linear systems. The corresponding controllability and observability decompositions are derived, and several concepts of controllability and observability for coordinated linear systems are introduced and discussed. These results are then combined to a definition and characterization of stabilizability via dynamic measurement feedback for this class of systems.     

Controller design for stabilizing bilinear systems with state-based switching

Some nonlinear systems can be approximated by switching bilinear systems. In this paper, we proposed a method to design state-based stabilizing controller for switching bilinear systems. Based on the similarity between switching bilinear systems and switching linear systems, corresponding switching linear systems are obtained for switching bilinear systems by applying state-based feedback control laws. Instead, we consider asymptotically stabilizing the corresponding switching linear system through solving a number of relaxed LMI conditions. Stabilizing controllers for switching bilinear systems can be derived based on the results of the corresponding switching linear systems. The stability of the controller is proved step by step through the decreasing of the multiple Lyapunov functions along the state trajectory. The effectiveness of the method is demonstrated by both a theoretical example and an example of urban traffic network with traffic signals.     

Reconstruction of possibilistic behavior systems

Reconstructability analysis is viewed as a process of investigating the possibilities of reconstructing desirable properties of overall systems from the knowledge of the corresponding properties of their various subsystems. The reconstructability analysis consists of procedures for generating meaningful reconstruction hypotheses, procedures for the evaluation of the reconstruction hypotheses, and procedures for making various decisions regarding the acceptance of evaluated reconstruction hypotheses, generation of additional reconstruction hypotheses, termination of the analysis and the like.The paper discusses the evaluation of reconstruction hypotheses when the systems under consideration are possibilistic behavior systems. It is shown that a principle of maximum ambiguity, similar to the principle of maximum entropy for probabilistic systems, can be used for possibilistic systems. It is also shown that the unbiased (maximum ambiguity) reconstruction can be determined by a simple join procedure, in a similar fashion as for probabilistic systems. The join procedure for possibilistic systems turns out to be computationally simpler than the one for probabilistic systems. The paper also describes a general procedure for determining the reconstruction family.     

Some problems of the linear theory of systems of ordinary differential equations

We consider problems of the linear theory of systems of ordinary differential equations related to the investigation of invariant hyperplanes of these systems, the notion of equivalence for these systems, and the Floquet–Lyapunov theory for periodic systems of linear equations. In particular, we introduce the notion of equivalence of systems of linear differential equations of different orders, propose a new formula of the Floquet form for periodic systems, and present the application of this formula to the introduction of amplitude–phase coordinates in a neighborhood of a periodic trajectory of a dynamical system.